In the paper we prove that an additive Darboux function f: R-->R can be expressed as a composition of two additive almost continuous (connectivity) functions if and only if either f is almost continuous (connectivity) function or dim(ker(f)) is not equal to 1. We also show that for every cardinal number K there exists an additive almost continuous functions with dim(ker(f))=K. A question whether every Darboux function f: R-->R can be expressed as a composition of two almost continuous functions remains open.
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Last modified May 15, 1998.